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Kleismic rank three family

Revision as of 22:16, 28 September 2010 by Wikispaces>genewardsmith (**Imported revision 166260967 - Original comment: **)

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Original Wikitext content:

These are the rank three temperaments tempering out the kleisma, 15625/15552. If nothing else is tempered out we have a 7-limit planar temperament, with an 11-limit comma we get an 11-limit temperament, and so forth.

7 and 9 limit minimax
[|1 0 0 0>, |0 1 0 0>, |1 5/6 0 0>, |0 0 0 1>]
Eigenmonzos: 2, 7/6, 4/3

Map: [<1 0 1 0|, <0 6 5 0|, <0 0 0 1|]
Generators: 2, 6/5, 7
Edos: 15, 19, 23, 34, 53, 68, 72, 87, 121, 125, 140, 212, 333, 405

===Enlil===
Commas: 15625/15552, 385/384

Minimax tuning
[|1 0 0 0 0>, |0 1 0 0 0>, |1 5/6 0 0 0>, 
|3 1/12 0 1/2 -1/2>, |3 1/12 0 -1/2 1/2>]
Eigenmonzos: 2, 4/3, 14/11

Map: [<1 0 1 0 6|, <0 6 5 0 1|, <0 0 0 1 -1|]
Generators: 2, 6/5, 7


13-limit
Commas: 15625/15552, 385/384, 325/324

13 and 15 limit minimax tuning
[|1 0 0 0 0 0>, |4/3 0 0 -2/9 -2/9 4/9>, 
|19/9 0 0 -5/27 -5/27 10/27>, 
|28/9 0 0 13/27 -14/27 1/27>, 
|28/9 0 0 -14/27 13/27 1/27>, 
|28/9 0 0 -14/27 -14/27 28/27>]
Eigenmonzos: 2, 13/11, 14/11

Map: [<1 0 1 0 6 0|, <0 6 5 0 1 14|, <0 0 0 1 -1 0|]
Generators: 2, 6/5, 7
Edos: 15, 19, 34, 53, 57, 68, 72, 87, 159, 212, 284, 299

Original HTML content:

<html><head><title>Kleismic rank three family</title></head><body>These are the rank three temperaments tempering out the kleisma, 15625/15552. If nothing else is tempered out we have a 7-limit planar temperament, with an 11-limit comma we get an 11-limit temperament, and so forth.<br />
<br />
7 and 9 limit minimax<br />
[|1 0 0 0&gt;, |0 1 0 0&gt;, |1 5/6 0 0&gt;, |0 0 0 1&gt;]<br />
Eigenmonzos: 2, 7/6, 4/3<br />
<br />
Map: [&lt;1 0 1 0|, &lt;0 6 5 0|, &lt;0 0 0 1|]<br />
Generators: 2, 6/5, 7<br />
Edos: 15, 19, 23, 34, 53, 68, 72, 87, 121, 125, 140, 212, 333, 405<br />
<br />
<!-- ws:start:WikiTextHeadingRule:0:&lt;h3&gt; --><h3 id="toc0"><a name="x--Enlil"></a><!-- ws:end:WikiTextHeadingRule:0 -->Enlil</h3>
Commas: 15625/15552, 385/384<br />
<br />
Minimax tuning<br />
[|1 0 0 0 0&gt;, |0 1 0 0 0&gt;, |1 5/6 0 0 0&gt;, <br />
|3 1/12 0 1/2 -1/2&gt;, |3 1/12 0 -1/2 1/2&gt;]<br />
Eigenmonzos: 2, 4/3, 14/11<br />
<br />
Map: [&lt;1 0 1 0 6|, &lt;0 6 5 0 1|, &lt;0 0 0 1 -1|]<br />
Generators: 2, 6/5, 7<br />
<br />
<br />
13-limit<br />
Commas: 15625/15552, 385/384, 325/324<br />
<br />
13 and 15 limit minimax tuning<br />
[|1 0 0 0 0 0&gt;, |4/3 0 0 -2/9 -2/9 4/9&gt;, <br />
|19/9 0 0 -5/27 -5/27 10/27&gt;, <br />
|28/9 0 0 13/27 -14/27 1/27&gt;, <br />
|28/9 0 0 -14/27 13/27 1/27&gt;, <br />
|28/9 0 0 -14/27 -14/27 28/27&gt;]<br />
Eigenmonzos: 2, 13/11, 14/11<br />
<br />
Map: [&lt;1 0 1 0 6 0|, &lt;0 6 5 0 1 14|, &lt;0 0 0 1 -1 0|]<br />
Generators: 2, 6/5, 7<br />
Edos: 15, 19, 34, 53, 57, 68, 72, 87, 159, 212, 284, 299</body></html>
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